For triangle ABD, tan (A) = 24/16; tan (B) = 16/24. So let's look those tangets up-- what angle's tangent is 1.5, and what angle's tangent is 0.666? Let's hope that the two angles we find add up to 90 degrees, because the left over angle (D) is 90 degrees only if 180 minus the sum of angles A and B is 90 degrees.

Yep, 14 and 76 = 90, so good. And since BC is a line (180 degrees), the angle on the other side of the altitude is also 90 degrees.